Paper ID sheet
- TITLE: Two-sided Grassmann-Rayleigh quotient iteration
- AUTHORS: P.-A. Absil, P. Van Dooren
- ABSTRACT:
The two-sided Rayleigh quotient iteration proposed by Ostrowski computes
a pair of corresponding left-right eigenvectors of a matrix $C$. We
propose a Grassmannian version of this iteration, i.e., its iterates are
pairs of $p$-dimensional subspaces instead of one-dimensional subspaces
in the classical case. The new iteration generically converges locally
cubically to the pairs of left-right $p$-dimensional invariant subspaces
of $C$. Moreover, Grassmannian versions of the Rayleigh quotient
iteration are given for the generalized Hermitian eigenproblem, the
Hamiltonian eigenproblem and the skew-Hamiltonian eigenproblem.
- KEY WORDS: Block Rayleigh quotient iteration, two-sided
iteration, Grassmann manifold, generalized eigenproblem,
Hamiltonian eigenproblem.
- STATUS: Numerische Mathematik, Volume 114, Number 4, pp. 549-571, February, 2010.
(Technical report UCL-INMA-2007.024.)
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BibTeX citation:
@ARTICLE{AbsDoo2010,
author = "P.-A. Absil and P. Van Dooren",
title = "Two-sided Grassmann-Rayleigh quotient iteration",
journal = "Numer. Math.",
fjournal = "Numerische Mathematik",
year = 2010,
month = "February",
volume = 114,
number = 4,
pages = "549-571",
}
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